probability density is maximum at the nucleus
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an electron can't be "inside" the nucleus. Think about it, the thing that keeps electrons from occupying the same space is other electrons. But there aren't (so-to-speak) other electrons in the nucleus... so there's no reason an electron can't just pass straight through as if it wasn't even there.
In fact, we use this idea to a degree in the notion of "muon-catalyzed fusion." Muons are heavy electrons. Thus their orbits are even more strongly peaked in the nucleus. Since the muon is more often in the nucleus, it "shields" the positive charge of the nucleus to a stronger degree, so nuclei are more like neutral particles to closer length scales. So then if I go to slam a muonic-hydrogen together with another muonic-hydrogen, they're able to get a lot closer with much less energy to push them together, meaning fusion can happen at lower energies than with electrons. (that being said, muons are hard to make, somewhat shortlived, so don't expect to see this as a viable form of power)
In fact, we use this idea to a degree in the notion of "muon-catalyzed fusion." Muons are heavy electrons. Thus their orbits are even more strongly peaked in the nucleus. Since the muon is more often in the nucleus, it "shields" the positive charge of the nucleus to a stronger degree, so nuclei are more like neutral particles to closer length scales. So then if I go to slam a muonic-hydrogen together with another muonic-hydrogen, they're able to get a lot closer with much less energy to push them together, meaning fusion can happen at lower energies than with electrons. (that being said, muons are hard to make, somewhat shortlived, so don't expect to see this as a viable form of power)
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